Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of this example tosketch the graph of f' below it.Oоy0о

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Answered: Trace or copy the graph of the given…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. As shown in Figure 2, a camera is mounted at a point 3000 ft from the base of a rocket launching pad. The rocket rises vertically when launched, and the camera's elevation angle is continually adjusted to follow the bottom of the rocket. (a) Express the height x as a function of the elevation angle 0. (b) Find the domain of the function in part (a). Rocket 3000 ft Camera Figure 2
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
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Identify the type of each of the following functions fromits equation. Then graph the function.
How would I use this graph of f to draw its inverse function?
2x Let h(x) = 3x- 4 a. Find the equation of the inverse function h-(x). b. State the domain and the range of h='(x).
Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 80 85 90 95 35 188 212 238 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. f(хо + Дх, Уо) -f (хо- Уo) if,(xo, yo) = lim Ay-0 f (x0, Yo + Ay) – f (xo. Yo) Ay f. (xo, Yo) = lim Ax-) Ax Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of r with respect to v when v = 85ft/s and 0 = 45°. dr i dv (b) Estimate the partial derivative of r with respect to 0 when v = 85ft/s and e = 45°. dr ANGLE O (degrees)

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Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of this example to sketch the graph of f' below it. O о y 0 O